الفهرس | Only 14 pages are availabe for public view |
Abstract Several ring theoretic properties of a ring naturally depend on the additive group of the ring. It is therefore an important task to study additive groups of rings with involution. The aim here is to investigate structural properties of rings with involution using the ground additive groups. The notions like –* cyclic groups, strongly principal* –ideal ring groups, strongly *- subdirectly irreducible ring groups are introduced and studied deeply. Ring theoretic properties of involution ring with ascending and descending chain conditions (acc and dcc) on *- ideals and *- biideals are also investigated. Utilizing the properties of nil and non-nil groups we posed several characterizations of torsion, torsion-free and mixed additive groups of involution rings. |